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Mar 21, 2023
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# MATH 147 Business Precalculus (5 credits)

Distribution Area Fulfilled Natural Sciences; Quantitative and Symbolic Reasoning; General Transfer Elective
Formerly MATH 147/MATH 156 Finite Mathematics

Prerequisite MATH 098  or equivalent with a grade of at least 2.0, or placement test score above MATH 098.

Course Description
Linear, polynomial and rational function models. Exponential and logarithmic functions. Mathematics of finance, matrices, linear programming, and set operations.

Student Outcomes
Rate of change (content A, B)
1. Calculate the rate of change of a linear function numerically, graphically, and symbolically.
2. Interpret the rate of change verbally and graphically, including interpretation in business applications.
3. Calculate and simplify the difference quotient for various types of functions including linear and quadratic functions.
Functions (content C, D)
4. Evaluate a function given as a graph, table, or formula, particularly using standard function notation f(x),including piecewise functions.
5. Evaluate and simplify composite functions.
Linear functions, equations, and inequalities (content A, B, C, D)
6. Determine the equation of a line given various information (two points, a point and the slope, a point and some information about the slope such as a parallel or perpendicular line).
7. Sketch the graph of a line given a point and the slope, or two points, with and without a calculator.
8. Graph piecewise linear function
9. Solve linear equations for a specified variable.
10. Determine the linear regression for a given set of data that is approximately linear and interpret its accuracy with a calculator.
11. Solve linear inequalities and show the solution graphically, symbolically (inequality notation, interval notation, or set notation), and verbally.

Polynomial and rational functions (content A, C, D, E)
12. Determine the domain and range of polynomial and rational functions, with and without a calculator.
13. Determine zeroes (x-intercepts), the vertex, and axis of symmetry for quadratic functions, and use this information along with the y-intercept to sketch the graph without a calculator.
14. Determine the quadratic function if given various items of information (x-intercepts and a point, or vertex and a point) with and without a calculator.
15. Sketch the graph of a polynomial, using all available information: degree, sign of the leading term, zeroes (x-intercepts), the y-intercept, and the multiplicity of repeated zeroes.
16. Determine vertical and horizontal asymptotes, zeroes (x-intercepts), open circles, and y-intercepts for rational functions and use this information along with test points to sketch the graph.
17. Solve polynomial and rational inequalities and show the solution graphically and symbolically (inequality notation, interval notation, or set notation).

Exponential and Logarithmic functions (content A, D, F)
18. Graph exponential functions and correctly interpret graphs of exponential functions.
19. Solve problems involving exponential growth and decay functions with and without a calculator.
20. Use the relationship between exponential functions and logarithms to rewrite an exponential in logarithmic form and vice versa.
21. Use properties of logarithms (exponent property, sum and difference properties) to solve exponential equations without a calculator.

Applications (content G)
22. Solve a variety of business applications including the following:
- Break-even analysis for linear revenue, cost, and profit functions
- Equilibrium points for linear or quadratic or rational demand and supply functions,
- Finding a linear cost, revenue, or profit function given information such as marginal cost, fixed cost, price per item,
- Finding maximum profit, maximum revenue, or minimum cost, for quadratic profit/revenue/cost functions.
23. Solve a variety of application problems using rational, polynomial, logarithmic, and exponential equations and inequalities involving business, and topics chosen from health, social and natural sciences.

Matrices (content G)
24. Use row operations and the Gauss-Jordan Method to solve linear systems.
25. Perform basic matrix operations to include adding, subtracting, and multiplying matrices with and without a calculator.

Linear Programming (content H)
26. Optimize the objective function, consider constraints, and use graphical techniques.
27. Set up linear programming problems (objective functions and constraint inequalities) from applications.

Set Operations (content J)
28. Determine the complement, intersection, and union of two or more sets.
29. Use Venn diagrams to solve application problems involving business, health, social and natural sciences data.

Finance (content K)
30. Use finance formulas to compute future value, present value, and compound interest (including annually, quarterly, weekly, and daily).
31. Compute future value, present value, simple interest, compound interest (including annually, quarterly, weekly, and daily), continuous interest, and amortization schedules for a variety of finance problems.

Writing
32. Use appropriate units when solving application problems. Express solutions to problems correctly in sentences, when appropriate. Use mathematical terms and vocabulary correctly.

General Skills
33. Communicate methods of solution and solutions to problems clearly to their intended audience.
34. Participate actively and responsibly in course activities.